Stochastic Rounding Implicitly Regularizes Tall-and-Thin Matrices

arXiv:2403.12278v1 Announce Type: new
Abstract: Motivated by the popularity of stochastic rounding in the context of machine learning and the training of large-scale deep neural network models, we consider stochastic nearness rounding of real matrices $\mathbf{A}$ with many more rows than columns. We provide novel theoretical evidence, supported by extensive experimental evaluation that, with high probability, the smallest singular value of a stochastically rounded matrix is well bounded away from zero -- regardless of how close $\mathbf{A}$ is to being …

abstract arxiv context cs.lg cs.na deep neural network evaluation evidence experimental machine machine learning math.na network neural network novel scale stochastic training type